I asked my current coach whether she could help me find a Dance partner. She only has male Ice Dance students. She said none of the coaches she knows well would be interested in that - coaches tend to want most of their students to pay the coach to dance with them. Obviously, that won't work for high level "amateur" competitive couples, but the coaches that specialize in that only work with a small number of other coaches.
She would like to start an ice dance class, which sounds like a good place to meet partners - but she teaches at rinks that don't have enough skaters to support a commercially viable ice dance class. The few adult ice dance classes I've found deal with the imbalance by not teaching partnering.
The fact that the vast majority of skaters are ladies doesn't help. USFSA allows men to skate pairs with men, and ladies with ladies - but they can't compete against the usual man/lady pairs. AFAICT most ladies don't want to be part of a female/female pair. Dance couples must have one lady and one man. (USFSA technical rules 5020, 6011.)
There are doubles events for kayaks and canoes. But it's easy to meet your partners - for safety reasons, people tend to paddle in groups, and often use training partners. Plus, rivals in singles events can get together for doubles events - and for mixed doubles, they still show up at the same competitions. I don't think the paddling styles are as incompatible as ice dance styles - though in canoes, the front and rear paddlers generally agree to switch sides with the same number of strokes between.
Two of the biggest things that make it easier in paddling are that there is no major reason you have to take from coaches of the opposite gender, so you can partner with other students of the same coach more easily, and there is no PSA to tell coaches they can't recruit other coach's students. It is done all the time, and it isn't considered unethical.
I don't have good solutions to these issues. Just saying.